Dynamic modeling of gene expression data

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Presentation transcript:

Dynamic modeling of gene expression data Neal S. Holter et. al. PNAS vol.98, No4, 2000 Summarized by Jinsan Yang

2002 SNU Biointelligence Lab. Introduction Assumptions The expression levels of genes at a given time are postulated to be linear combinations of their levels of at a previous time Common Goals Describe the time evolution of gene expression levels by using a time translation matrix Derive the time translation matrix by using characteristic modes of SVD (singular value decomposition) 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Introduction Notes Time translation matrix reflects the magnitude of the connectivities between genes The number of genes g far exceeds the number of time points (g x g equations are needed – ill posed problem) Nonlinear interpolation scheme: speculative Clustering genes: not clear In this paper: Use characteristic modes from SVD The casual links between the modes (hence for genes) involve just a few essential connections and any additional connections are redundant 2002 SNU Biointelligence Lab.

Singular Value Decomposition (SVD) Singular value decomposition of an (n x m) matrix A : m: gene number, n: time interval number columns of U (gene coefficient vectors) form a orthogonal basis for the gene space a columns of V (gene expression vectors) form an orthogonal basis for the expression (array) space 2002 SNU Biointelligence Lab.

Singular Value Decomposition (SVD) Calculating SVD of A : from the eigen values of AA and AA Smaller singular values correspond to ‘noise’, larger singular values correspond to principle directions in the data The columns of U are determined by The vectors (modes) are the first r rows of the matrix where each column corresponds to the times at which the corresponding expression data are measured The temporal variation of any gene j can be written exactly as a linear combination of these r characteristic modes as 2002 SNU Biointelligence Lab.

Singular Value Decomposition (SVD) For any gene j : The contribution of the first k modes to the temporal pattern of a gene j and its average over all genes : 2002 SNU Biointelligence Lab.

Singular Value Decomposition (SVD) 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Method Expression levels of r modes at time t : The linear model: The gene expression data set can be reexpressed precisely by using the r specific coefficients for each gene, M, and the initial values of each of the r modes. M can be derived by using simulated annealing methods M(i,j) describes the influence of mode j on mode i M(i,j) multiplied by the expression level of gene j at time t contributes to the expression level of gene i at time (t+t ) 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Results Datasets: yeast cell cycle (CDC15) (15) yeast sporulation (7) Human fibroblast (13) Reducing the number of modes: from the matrix M from r clusters of genes: six clusters of yeast sporulation data: Metabolic, early I, early II, middle, midlate, late 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Results The expression of 6 clusters by six modes: The interrelationships between the cluster expression patterns: measured (o) and calculated (-) expression profiles 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Results For (2 x 2) M matrix from the matrix M using 2 most important modes a: 2x2 translation matrix from initial values b: linear combination of 2 modes c: original data 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Results 2002 SNU Biointelligence Lab.

2002 SNU Biointelligence Lab. Results 2002 SNU Biointelligence Lab.